Thanks to Nils and Robert for their quick responses. This is definitely
one thing to love about SciPy. I posted my null space question
yesterday and Robert responded in 20 minutes and Nils in 30. I posted
my optimization question this morning and Nils reponded in 8 minutes!
It is almost like chatting with tech support. You make SciPy a pleasure
to use! Thanks.
Coincidentally, these two problems are linked and I don't know if my
numerical error problems are from fmin or the null space/svd stuff.
Once I find the input that drives my matrix to have a null space, I find
the vector that corresponds to the null space (assuming the sub-matrix
is only rank deficient by 1). Then I combined the null space vector
with zeros that correspond with the boundary condition on one end of the
problem. So, a 4x1 null space vector would give me an 8x1 full vector.
I then take the 8x8 full matrix which has a 4x4 submatrix whose
determinant is roughly 0 and multiply it by the 8x1 vector of the
boudnary conditions I just solved for. This should then give me an 8x1
vector of the boundary conditions on the other end. The problem is that
there are some elements of this second vector that should be 0 because
of the boundary conditions and they are actually of order 1e-10, if the
vector is normalized so that its magnitude is 1. This physically means
that I have a cantilever beam with a free end that has just a little bit
of force and moment at the free tip.
Ryan
Ryan Krauss wrote:
> The matrix is currently 4x4 but will grow to probably 6x6. It is
> definitely nonlinear. The matrix contains sinh, cosh, sin, and cos.
> I am using the transfer matrix method to analyze structures. When you
> say two-parameter, do you mean the real and imaginary part of the
> independent variable? I guess you are right that I don't necessarily
> need to use the determinant. In order to satisfy the boundary
> conditions of the problem this 4x4 or 6x6 matrix (which is really a
> submatrix of an 8x8 or 12x12) must have a null space. So, what would
> be the better thing to look for? An eignevalue that approaches 0?
>> Ryan
>> Nils Wagner wrote:
>>> Ryan Krauss wrote:
>>>>> I have a matrix that is a function of a complex valued input. I am
>>> trying to find that value of that input that drives the determinant
>>> of the matrix to zero. I am searching for this value using fmin.
>>> The error I am trying to minimize is the abs(det(complex matrix)).
>>>>>>>> It's not a good idea to use the determinant directly since det(A) is
>> a rapidly varying function. As far as I understand your problem,
>> you are interested in the solution of a two-parameter nonlinear
>> eigenvalue problem. Is that correct ? How about the size of your
>> complex matrix A ?
>>>> Nils
>>>>> I don't seem to be able to drive this error lower that roughly
>>> 9e-17, regardless of the values for ftol and xtol I use.
>>>>>> Am I hitting some internal limitation? Are complex values by
>>> default single or double precision?
>>>>>> Thanks,
>>>>>> Ryan
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